Labs septic

In mathematics, the Labs septic surface is a degree-7 (septic) nodal surface with 99 nodes found by Labs (2006). As of 2015, it has the largest known number of nodes of a degree-7 surface, though this number is still less than the best known upper bound of 104 nodes given by Varchenko (1983).^[1]

3D model of affine chart of the real Labs septic

See also

• Barth surface
• Endrass surface
• Sarti surface
• Togliatti surface

References

1. The upper bound in degree 7 given by Giventalʹ (1983) is 106.

• Giventalʹ, A. B. (1983), "The maximum number of singular points on a projective hypersurface", Funktsionalʹnyĭ Analiz i ego Prilozheniya, 17 (3): 73–74, MR 0714227
• Labs, Oliver (2006), "A septic with 99 real nodes", Rend. Semin. Mat. Univ. Padova, 116: 299–313, arXiv:math/0409348, Bibcode:2004math......9348L, MR 2287352
• Varchenko, A. N. (1983), "Semicontinuity of the spectrum and an upper bound for the number of singular points of the projective hypersurface", Doklady Akademii Nauk SSSR, 270 (6): 1294–1297, MR 0712934

External links

• Bothmer, video of Labs septic